These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
The board game:
Goddamn Bats: The 2-peg boat is this. Its small profile allows a lucky player to turn around the entire game even if they're at a disadvantage. Conversely, managing to sink the thing early on makes winning a whole lot easier.
Alternate Character Interpretation: The aliens, as possibly a peaceful expedition. They repeatedly avoid harming non-threatening humans and only fire when fired upon, which raises the possibility that they were not invaders or scouting for an attack but peaceful, and twitchy humans botched first contact.
Additional evidence: the alien's sole projectile weapon is effectively a large-scale grenade launcher with less range and firepower than any modern weapon seen; no infantry-scale alien has a ranged weapon, and the "weapons" used more resemble tools; their single most dangerous weapon, the chainsaw-balls, are used extremely sparingly, usually as a last resort, and are also melee weapons.
According to the novelization, this is explicitly incorrect, and the alien force was here to determine how much strength will be needed to overwhelm Earth's resistance. How they'll respond with no word back is up in the air.
There's more evidence in the film though if you look at it right, after all they launched an attack on the island unprovoked, taking out highways and KILLING the students at the sat array so they could take it over as their communication hub. sure if a enemy puts down their weapons they stand down but isn't that pretty normal rules of war, not to kill civilians and those (seemingly) surrendering? Or are you saying that air force base that was minding it's own business and the highways were inciting the aliens?
Fridge Horror: So yeah, the day is saved, but think about it. This is an organized military invading Earth, that lost its means of communication. Sooner or later search and rescue parties are going to be sent, and as soon as they get word out about us...
Fridge Logic: Wait, how did they get the Missouri fueled, loaded, and generally back into fighting condition in only a few hours?
Is this the first time that a movie's very existence, even on the most basic conceptual level, been so narmy?
The scene with the veterans stepping up to help prepare and launch the Missouri again, especially when aged veterans in an ancient ship dramatically outperform modern vessels against the aliens. Goes straight into Narm Charm for some.
Nightmare Fuel: The shots of the interior of the Samson taking on water after being hit by the aliens' weaponry, which includes sailors yelling for help as the compartments they're in start to fill up.
Tearjerker: Stone's death. Made even worse when you remember that the last thing Alex said to him was "I'm sorry I let you down." And the last shot of him is standing on the ship's deck, scanning the seas for Alex.